Passive Dendrites and Cable Filtering

How to use the simulation

Start with the distal alpha-current input. Compare the local input response with the dendrite-recording and soma traces. Drag the animation-time slider or select Animate to watch voltage spread along the cable, then move the input toward the soma.

Try these: increase dendrite length; reduce diameter; increase axial resistance R_a; change R_m or C_m; then enable dendrite B to make a controlled comparison.

What the model shows

A passive dendrite is both a resistor and a capacitor. Current spreads longitudinally through the cytoplasm while leaking through, and charging, the membrane. Consequently, a signal normally becomes smaller, later, and broader as recording distance increases. The spatial profile reveals attenuation along the cable at the selected time. Its voltage axis is fixed from the minimum and maximum found over the complete simulation, so apparent changes cannot be caused by rescaling. During animation, the voltage traces grow up to the moving time cursor while the spatial profile shows the voltage everywhere at that same moment.

The membrane time constant is τ_m = R_mC_m. For a uniform cylindrical cable, the displayed steady-state length constant is λ = √(dR_m/4R_a). Electrotonic distance x/λ expresses physical distance in units that reflect the cable properties. The finite cable and soma mean that transient attenuation is not simply e^−x/λ.

Suggested exercises

1. Location: move the same input from distal dendrite to soma. Compare peak amplitude, peak time, and waveform width.
2. Morphology: compare thin and thick dendrites. Predict the change in λ before viewing the traces.
3. Membrane versus cytoplasm: vary R_m, C_m, and R_a separately. Decide which property changes λ, τ_m, or both.
4. Low-pass filtering: compare a brief alpha current with longer square pulses. Fast changes are attenuated more strongly with distance.
5. Space clamp: place the input distally and inspect the simultaneous voltage gradient. A somatic voltage measurement cannot imply that the whole dendrite has the same voltage.

Scope and assumptions

The simulation uses a uniform, unbranched, sealed-end passive cable attached to a 20-µm spherical soma. It solves a compartmental cable model with an implicit numerical method. The stimulus is prescribed current, which isolates cable filtering from changes in synaptic driving force. There are no voltage-gated conductances, dendritic spines, branching, or conductance-based synapses. These choices make causal comparisons clear, but the model is not a reconstruction of a particular neuron.

References

Rall W (1959), Branching dendritic trees and motoneuron membrane resistivity. Experimental Neurology 1:491–527.

Rall W (1962), Electrophysiology of a dendritic neuron model. Biophysical Journal 2:145–167.

Rall W (1967), Distinguishing theoretical synaptic potentials computed for different soma-dendritic distributions of synaptic input. Journal of Neurophysiology 30:1138–1168.